3.4 图38 证此国理的证明和别理31的证明相道,因为/d2=12-61),所以 (z)dz-i(62-61) [2()-6}/≤)|1()-6, 由于当61≤arga≤B2,2→∞时,2f(2)-一间单连于K,这意hv>0,3(与argz无关 的)M()>0,使当|2=R>M时,|zf(z) f(a)dz-ik(02-01)sE(02-01), f(2)dz=ik(2-1) R§3.4 ↔↕➙➛✂➜☎ ✞ 10 ✟ ❋ 3.8 Ô ✼➝➀✢Û Ü✶ ➊ ➚ 3.1 ✢Û Ü❬➞✤◆✱ Z CR dz z = i￾ θ2 − θ1
✧✏ Ï     Z CR f(z) dz − iK(θ2 − θ1)     =     Z CR  f(z) − K z  dz     =     Z CR zf(z) − K dz z     ≤ Z CR  zf(z) − K   · |dz| |z| . ⑦❥✸ θ1 ≤ arg z ≤ θ2 ✧ z → ∞ ✻ ✧ zf(z) ✴➋➄➌➍❥ K ✧❐✯➔→ ∀ε > 0 ✧ ∃(❁ arg z ❄❅ ✢ ) M(ε) > 0 ✧✹✸ |z| = R > M ✻ ✧ |zf(z) − K| < ε ✤✏ Ï     Z CR f(z) dz − iK ￾ θ2 − θ1
    ≤ ε(θ2 − θ1), ♦ lim R→∞ Z CR f(z) dz = iK ￾ θ2 − θ1
.